Question: Gabriela is 30 years younger than Omar. For the last four years, Omar and Gabriela have been going to the same school. Eighteen years ago, Omar was 4 times as old as Gabriela. How old is Omar now?
Explanation: We can use the given information to write down two equations that describe the ages of Omar and Gabriela. Let Omar's current age be $o$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $o = g + 30$ Eighteen years ago, Omar was $o - 18$ years old, and Gabriela was $g - 18$ years old. The information in the second sentence can be expressed in the following equation: $o - 18 = 4(g - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = o - 30$ . Substituting this into our second equation, we get the equation: $o - 18 = 4($ $(o - 30)$ $ -$ $ 18)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 18 = 4o - 192$ Solving for $o$ , we get: $3 o = 174$ $o = 58$.